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Pythagoras of SamosAuthor(s): Howard BakerSource: The Sewanee Review, Vol. 80, No. 1 (Winter, 1972), pp. 1-38Published by: Johns Hopkins University PressStable URL: http://www.jstor.org/stable/27542596Accessed: 11-03-2016 14:10 UTC
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PYTHAGORAS OF SAMOS
By HOWARD BAKER
THE first person ever to adopt the name philosopher comes
down to us looking the most bizarre. An uncommonly
big rosy man with an elegant cloak and a handsome beard,
he is reported also to have had a golden leg, a flighty head for
mathematics, an ingenuous belief in metempsychosis, and the
power of working miracles. The guardians of the memory of
Pythagoras have contrived a fantastic legend about him. It is
just about as fantastic as the legend with which Aesop the fabulist
was immortalized, only it goes toward the opposite extreme,
Apollonian beauty rather than Satyric ugliness, and has been even
more puzzling to sober keepers of old records than the Aesop
legend.
Although traditional history gathers encrustments which can
not be removed, I have hopes of restoring the outline of the per
son Pythagoras must have been by considering him strictly in the
light of his Ionian origins. His origins are the primary fact
about him: he was an Ionian of the island of Samos, an Ionian
who migrated westward, it is true, and settled in Italy in a strange
intellectual climate ; but he was "quite old enough", in the esti
mate of W, K. C. Guthrie, "to have studied mathematics before
he left the East, where a strong mathematical tradition con
tinued . . . no less, if not more, than in . . . the West".
For Herodotus?, and for his closest contemporaries, he was
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PYTHAGORAS OF SAMOS
PYTHAGORES OF SAMOS, spelled out like that with the E
in Ionic Greek. It follows that he was one of the close small
family of the earliest Ionian philosophers?Thaies, Anaximander,
Anaximenes, Heraclitus. . . . He was basically in agreement with
them -j and he was not by any means the least of them either, as
Herodotus goes out of his way to remark.
But he remained, like the other Ionians, more or less a stranger
to what became the Athenian tradition in philosophy. Pythag
oras's tradition was the tradition of Democritus, "who went to
Athens and nobody knew him".; and I don't mean the Democritus
of atomism so much as of the whole complex archaic inquiry
which gave rise incidentally to the theory of the atom. The shape
which this inquiry casts backwards onto the shadowy presence of
Pythagoras is what this essay is about.
My real concern of course is with something more than putting
together a jigsaw-puzzle portrait of an imposing personage with
Samian features. In Pythagoras, probably for the first time in
history, a human mind attempted to achieve a wholly objective
conquest of the many-faceted structure which is our universe; and
in the course of doing so, it discovered the mind's plight. Along
with positive insight into things taken separately and individually,
Pythagoras encountered an inherent principle of negativity,
summed up in irrational numbers, which implied that things on
the whole did not hang intelligibly together. To this day the
problem in the form of many sorts of indeterminacy is still deeply
troubling.1
indeterminacy: in science, e.g. quantum theory; in philosophy, e.g. linguistic
ambiguities, as in the verb to be. For the Pythagorean mathematical problem, see
P.-H. Michel, De Pythagore ? Euclide. For general matters, one has to use Diels
Kranz, Die Fragmente . . . , together with standard lexicons and the now numerous
explications of the relevant texts. The more recent books on Pythagoras, such as
J. A. Philip's Pythagoras and Early Pythagore anism, take off from a point of view
different from mine. In the case of Philip, it is Aristotle, whose characterizations I
try to avoid. In this connection, see, cum grano salis if you must, Harold Cherniss,
Aristotle9s Criticism. . . . Although most references should be easily identified from
my text, I must acknowledge a running contact with the works of Thomas Heath,
particularly Euclid's Elements and Aristarchus of Samos.
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HOWARD BAKER
3
II
In view of the irregular presumptions which guide the present
account, it won't be inappropriate to take our first look at Pythag
oras through the eyes of Lucian of Samosata. For all of his
glittering malice, the satirist Lucian has the solidest of merits,
and I regard his entrance here at the outset of our affair as pecu
liarly suitable, because for Shakespeare, for Ben Jonson, for every
body in the bright days of the Renaissance, Pythagoras was known
almost exclusively as the vaguely preposterous character in
Lucianas sketches.
The philosopher Lucian writes about had arrived at midphase
in the development of his legend; he's already much overblown
but not yet divorced from his original humanity. The following
is a sample of the sort of amiable caricature for which Lucian is
responsible. It is an excerpt from "Philosophies on the Auction
Block", in which the satirist imagines Zeus as putting various
systems of philosophy up for sale for the benefit of mankind. The
scene is a sales arena; the auctioneer is Hermes. Acting as im
personations of their doctrines, the founders of the philosophic
schools come up one by one for auction, and, while the buyers
consider them, they expound their views and make what claims
they can to recommend themselves and their doctrines. Here,
in slightly condensed paraphrase, are the negotiations involving
Pythagoras, The dialogue amounts to an epitome, a motley but
sound epitome, of the Pythagorean creed in a second-century
A.D. guise.
Hermes (to Zeus)
Who shall we put up first?
Zeus
The one with the long hair. The Ionian. He shows off
pretty well.
Hermes (to Pythagoras)
Come up here.
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4 PYTHAGORAS OF SAMOS
Zeus
All right, sell him.
Hermes
Here, gentlemen, this one's tops Who'll buy him? Who's
for superman? Harmony of the universe? Music of the
spheres? Who'll bid for the transmigration of souls?
Buyer
He looks all right, but what can he do?
Hermes
Arithmetic, astronomy, falsifications, geometry, folk
songs. . . . He's good at picking futures, and great at group
therapy.
Buyer (to Pythagoras)
Where are you from?
Pythagoras
Samos.
Buyer
Where did you go to school?
Pythagoras
To the Sages, in Egypt.
Buyer
If Pd buy you, what would you teach me?
Pythagoras
Nothing. But Pd help you get started remembering some
things.
Buyer
How would you do that?
Pythagoras
First Pd make you freshen up your soul.
Buyer
How?
Pythagoras
By requiring you to keep silent. For five years you'd keep
perfectly still.
Buyer
Look, maybe you'd better get yourself sold to Croesus, to
teach that deaf and dumb son of his?But if I buy you, what
after that?
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PYTHAGORAS OF SAMOS
you look like. By Heracles his thigh is solid gold Pll
take him What do you want for him? Ten minas? He's
mine
Zeus (to Hermes)
Get the buyer's name.
Hermes
He seems to be an Italian, Zeus, from Crot?n ... or Taren
tum. . . .
Ill
Just under the flamboyant surface of Lucian's dialogue, there
is a straightforward review of Pythagorean topics. The trans
lation of the long-haired Ionian to the rich, restless Greek cities
at the bottom of Italy is basic history. As for the pack of doc
trine which he took with him, the range of his teachings and the
peculiar variety in its content are represented fairly enough,
though the language is the language of clowning. But even so,
according to the brilliant study of Lucian by J. Bompaire, the
gaudiness of the expression derives in part from the professional
rhetoricians, who loved to make lectures on Pythagoras, and, in
another part, from the shoddy teaching slogans resorted to by
the Pythagoreans themselves. Either way the creed became a
patchwork of inflated clich?s, which Lucian is only too happy to
put on display. He lets the crudest claims of the cult ridicule
the cult itself; and that's a sound measure of his true genius.
Eventually the cult invented extravagances which must have
exceeded anything that Lucian knew about. He does not men
tion, for instance, the late neo-Platonic claims that Pythagoras
possessed some very picturesque divine powers. In regard to the
supposed connection of the Master with the Supernatural, here is
what lamblicus says with a straight face about the later Pythag
oreans:
They thought their opinions deserved to be believed, be
cause he who first promulgated them was not any casual
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HOWARD BAKER
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person but a God. For this was one of their questions: What
was Pythagoras? For they say that he was the Hyperborean
Apollo; of which this was an indication, that rising up in
the Olympic games, he showed his golden thigh ; and also
that he received the Hyperborean Abaris as his guest, and
was presented by him with the dart on which he rode
through the air. . . .
Et cetera, et cetera: he conversed with animals, handled snakes,
appeared in more than one city at exactly the same hour of the
same day.
"Gods make all things possible," the neo-Platonists argued,
and to top all potential absurdities in the argument, the Suidas
describes a late Medieval rite called the Pythagus, in which words
written in blood on a mirror are read in the reflected image of
the full moon, with certain edifying results.
Obviously the stream of the legend has left its fountain sources
so far behind that nothing pertaining to Ionian philosophy has
come down in it. This is not surprising. If we are aware of the
difficulty of expressing any distinct idea aptly, with no slanting at
all, we certainly can't be blind to the difficulties of transmitting
philosophical ideas from generation to generation. When the
ideas take popular, activist forms, the difficulties are all but in
surmountable. Think of what has happened to Existentialism in
the few decades between Sartre and the Hippies. While the topics
remain firm, the slogans and badges and anecdotes and lurid
applications change with the weather.
But on the island of Samos the memory of Pythagoras bore a
very different sort of fruit. In the third century A.D., some
seven centuries after Pythagoras's death, a large Imperial bronze
coin was struck on which was depicted a seated man surrounded by
the legend PYTHAGORES SAMION. The chair he sits in is
a heavily carved massive stool, a throne by convention. A robe
is wrapped around his lower body, with a corner hanging over
his left shoulder. His hair is bound around with a circlet.
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PYTHAGORAS OF SAMOS
Lodged in his left arm is a staff. He is leaning aggressively for
ward toward a sphere mounted on a pedestal, applying a flat
object, perhaps a disc with its edge toward us, to the surface of
the sphere. He appears to be in a deep study of the mathematical
problem which Democritus stated in one of his titles: "On the
Contact of Circle and Sphere"?i.e.> a sort of irrational angle
called the Horn-angle.
The man commemorated is the founder of systematic geome
try. I suppose it is no accident that this portrait resembles copies
of Pheidias's Zeus which were struck on many Imperial coins.
The implications are self-evident. "He's also a god who first
discovered Wisdom. . . ," as Lucretius said of Epicurus, a god of
totally different powers, however, from him who soared around
through the heavens on Apollo's golden arrow. The effect of
the coin is to extricate Pythagoras from legend and neo-Platonism,
and to restore him to the beaches of Samos where, drawing geo
metric figures in the sand with his staff, he properly belongs.
IV
He was born and raised in Samos in a period when the Sardis of
Croesus dominated the Eastern world, and the Egypt of Amasis
the southern Mediterranean. Samos had important ties in both
directions, most conspicuously in Egypt, where in the Greek
settlement of Naucratis the Samians were numerous enough to
have a precinct of their own dedicated to Hera. Pythagoras, it
is said repeatedly, undertook extensive travels in the pursuit of
his early studies. Although similar excursions are attributed
right and left to the Sages, there is no reason to think that a man
as strongly attracted to a wide range of knowledge as Pythagoras
was would be less mobile than the multitudinous visitors to
oracles and games and festivals, or the innumerable merchants
and colonizers and adventurers of the sixth century, of whom
Sappho's brother, Charaxus, is only one interesting example.
Herodotus says very deliberately that, when Sardis was in its
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HOWARD BAKER 9
heyday, aall of the learned men of Hellas" came together there,
as the chances of life and opportunity permitted. And many
voyaged to Egypt; Solon, we believe, was one, Tha?es, another.
But the surest instance of an inquiring traveler is Herodotus
himself. So, most likely, Pythagoras did set off in his own time
in his own way and, as Lucian says, went to school to the Sages,
in Egypt. If so, he need not have been touched significantly by
Egyptian religious practices, any more than Herodotus was, or
any more than Eudoxus of Cnidus was, despite insinuations to the
contrary which seem to stem from the Athenian schools.
In Egypt he would have learned something a little more
complicated, however, than "the art of measuring land" which is
specified by Herodotus, for along with the re-surveys of the
boundary lines that had been swept from the fields by the annual
flooding of the Nile went further geometrical and astronomical
procedures on which could be founded an accurate calendar of
the rise and the fall of the river?the phenomenon that con
trolled the whole flow of Egyptian life. Even the placing of
the monster pyramids seems to be related to the problem of
determining the solstices and equinoxes and the heliacal rising of
certain stars v/hose advent meant that this or that stage of the
river was going to be now at hand.
In Sardis, with Mesopotamia looming large in the background,
he would have found similar versions of the same sciences, and
along with them apparently an even more brusque challenge in
the form of star-charts, coinage in precious metals, a wide variety
of art-works, a vivid mythology, bustling commercial enter
prises, philosophic debates, and grandiose political intrigues.
But simply as a Samian Pythagoras must have had the ad
vantage of being a combatant in the prolonged, jarring discus
sions which went on in his immediate corner of the world, where
Miletus, just across a narrow blue strait and a barren rocky
ridge, was the particularly famous theater of learning. In other
words, he was one of the tribe fathered by Tha?es-?it could not be
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PYTHAGORAS OF SAMOS
otherwise. He was one of the new cosmologists who looked for
instruction to the circling stars and circulating winds and spiraling
eddies in the muddy currents of the Meander. They were
sailor-farmers, warrior-merchants, these philosophers, enjoying
a small respite from the furious exertions ordinarily required
just to maintain life, and, having the time to look around at things,
they concentrated on natural things; they were not atheistic in
their materialism, but not animistic either in their interest in na
ture, as has been supposed simply on the basis of their archaic
language. They were witty pessimists, trying to understand life
and to make the most of it. It was a rare interval in the world's
history.
A man named Mnescharus, gem-engraver, was the father of
Pythagoras according to a story which seems to originate in the
Samian annals of Duris. Gem-engraving, in any event, was a
specialty of the high archaic period, when the artist-craftsman was
held in particular esteem. Another engraver of gems, Theodoras
of Samos, became renowned for a chariot-and-four which he
carved on a tiny seal-stone?almost as renowned as for his
Gargantuan labors in designing and building the colossal temple
of Hera, about which he is said to have published a book, possibly
the first treatise on architecture ever to be written.
On the whole the pre-Classical interval in Samos was illumi
nated by the poetry of Anacreon ; by incredible feats of engineer
ing; by scientific animal breeding; by an array of sculpture scat
tered over the island; by the systematic practice of medicine; by
compilations of astronomical and mathematical data; in short,
by the arts and works sponsored by Polycrates the Tyrant.
This brings us to the crux in our insubstantial biography of
Pythagoras. At the height of Samos's glory, her greatest orna
ment left Samos for Italy, because, it is said, of his hatred of
tyranny. Coming from Aristoxenus, this report could be taken
as a doctrinaire condemnation of a popular leader, such as Polyc
rates undeniably was; but what makes skepticism a little awk
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HOWARD BAKER
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ward here is an incident which Athenaeus recounts in his table
topics. Once, Athenaeus says, Polycrates, thinking he had rea
son to fear a conspiracy, went so far as to burn down the wrestling
schools of Samos because he suspected them of being the "counter
walls to his own citadel". Since a wrestling school was the
equivalent of any school and Pythagoras was a teacher, and since
at some undetermined date after Polycrates had seized power
Pythagoras moved away to Italy and became a famous teacher in
the politically oriented gymnasia of Crot?n, it does seem possible
that in Samos he may have got mixed up with the wrong party
and ended by exiling himself from his native island.
V
In Samos Pythagoras was beyond all doubt the natural phi
losopher, "investigating the laws", in the words of Vitruvius,
"and the working of the laws by which nature governs"; and
not overly concerning himself apparently with the edicts of
mortal rulers.
Regardless of his place of residence he continued to be at home,
in my opinion, in a well-defined intellectual setting, the bound
aries of which were strictly Ionian. Vitruvius, the Latin writer
on architecture (whose credentials as an authority on archaic
Greek matters I'll come to in a moment), puts Pythagoras in a
group with Tha?es, Xenophanes, Anaxagoras, and Democritus,
naming the five of them as the first who studied, among other
phenomena, the motions of the stars, not (like the Chaldeans) to
cast nativities, but to know the seasons better and the patterns of
the weather. Vitruvius, loyal Roman that he is, shows respect
for astrology; but for calendars and meteorological matters he
has an enthusiasm born of close acquaintance with life in the sea
girt settlements of the ancient Mediterranean world: witness his
anxiety about the way in which the long-prevailing seasonal
winds can funnel dust and debris through the streets of a city.
He has exactly this sort of concrete appreciation of the Pythag
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PYTHAGORAS OF SAMOS
orean triangle, and even of irrational numbers; of the use of
the compass and plumb-bob and gnomon; of the curvature of
the earth and the march of the constellations through the
heavens?and he is the first, I think, to try to translate into
writing the whole glorious panoply of the early sciences.
With a sturdy but graceless art Vitruvius reveals a tactile
sense of the things with which Pythagoras was concerned. For
us, this is all the more informative because it is not colored by
any doctrine or any of the partisanships of the schools, or any
astonishing individual genius of his own. Nevertheless, his errors
have been underscored while his good sense on most topics has
been overlooked, as on occasion it seems to be in Jean Soubitan's
finely elaborated new Bud? edition of Book IX of the famous
Ten Books on Architecture. Vitruvius's point of view, at the
wrorst, is unconventional. The early investigations of nature
had slashed a road open, he seems to believe, that led to Democri
tus and Eudoxus, and from them to Archimedes: a route that
for all practical purposes bypasses the metaphysical bailiwicks of
Plato and Aristotle, and the dialectical preserves of the Eleatics
as well. Therein, I am convinced, lie both the distinction and
the disrepute of Vitruvius,
But what we are finally interested in is the evidence for the
persistence of Ionian thinking in Pythagoras himself and in his
closest followers, despite the deviations which many of the Ital
ians pursued so ardently. Vitruvius assumes the fundamentally
Ionian position as a matter of course. Other evidence is not
wanting. The Samian historian of the end of the fourth century
B.C., Duris, is quoted in Porphyry to the effect that the son of
Pythagoras, Arimnestus, maintained Samian connections and was
besides the teacher of Democritus. Duris documents his state
ment by describing an imposing bronze tablet in the Samian
Heraion which bore a formal epigram, in which the monument
speaks as follows:
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Me Arimnestus, who much learning traced,
Pythagoras' beloved son, here placed.
(trans. T. Stanley)
To the information that this man Arimnestus was tutor to Democ
ritus, possibly during the period of Arimnestus's exile in Abdera,
Duris adds a fascinating footnote. Someone named Simos, Duris
says, was guilty of the theft of one of the seven Pythagorean
arts?the stolen one being the art of music?which had been in
scribed in canonic form on the bronze tablet erected in the temple,
and by publishing the theft as his own work, he had destroyed
the harmony of the whole.
Or something very much of that purport: the passage is diffi
cult and I've fallen back on Thomas Stanley's old interpretation
of it. However fanciful Duris may sound, the record of a bronze
monument of this sort in Samos substantiates the theory of a
continuing existence of an East Greek intellectual discipline, to
which Democritus obviously adhered. And Duris's epilogue has
what seems to me to be a wholly unexpected value. It tells us
exactly what the final intent of Pythagoras was. The great Samian
aspired to nothing less than the accumulation and perfect har
monization of all knowledge, of all "seven branches" of what
can be known.
That, of course, is just what Heraclitus held against him: the
fact that he was a confirmed polymath, an inquirer?his Ephesian
neighbor contended?who outstripped all men, who grasped at
all learning, but got nothing better in return?his critic was per
suaded?than a handful of frivolous results. Clearly the fierce
concentration of Heraclitus's mind would automatically reject the
ambition of a. Pythagoras to attain universal knowledge. But in
an archaic age, when it was presumed that the comprehension of
all things was within reach of the human intellect, that ambition,
though continually falling short of confident fulfillment, was
nevertheless the begetter of spectacular results; and with the
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PYTHAGORAS OF SAMOS
eventual realization that its ultimate failure was inevitable, there
came a sense of betrayal, like death.
At first, though, it appeared to be otherwise. At first all
branches of science seemed to flourish together, like the espalier
of a vine on an arbor.
VI
An early document dealing with Pythagoras, and in my opinion
one of the most genuinely instructive, is certainly one of the most
dazzling. This is hardly surprising, since it is a page which has
survived from the work of the poet Callimachus, a favorite model
for the poets of Roman Italy and, in brilliant, scholarly, third
century B.C. Alexandria, a fastidious authority on the books and
the arts of the past. The fragment I have in mind occurs in the
first of the Iambi; its facts, it is said, were taken from the Ionian
historian Maeandrius of Miletus. It recounts a version of the
ancient story in which someone travels the world over, hoping to
discover the wisest of the Sages in order to honor him with a
splendid award, in this case a golden cup. Each Sage, however,
modestly disclaims his own preeminence, so that eventually the
prize is set up as a dedication in a temple of Apollo.
In Callimachus's surviving verses Tha?es of Miletus is pro
posed as the leading candidate for the prize. But such are the
involutions of Callimachus's artistry that it is not Thaies so much
as Pythagoras who turns out to be the wise man far excellence.
Tha?es is granted a share of Pythagoras's glories: he is pictured
as being a studious follower of Pythagoras. The chronological
absurdity of this sequence is overcome by making Pythagoras
and Euphorbus, a Phrygian of Trojan times, one and the same
person under a poetic license derived from the doctrine of the
transmigration of souls. What Callimachus seems to suggest is
the fact that Pythagoras soon became the great master of the
arts with which Tha?es had been preoccupied: which is an en
tirely legitimate proposition.
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and Pythagoras, the poet Aratus explains the Phoenician prefer
ence for the Lesser Wain?or Bear?or Dipper (the name has
varied) as the constellation marking true north: its orbit had
the advantage of being smaller than that of the sprawling Great
Bear?or Wain?or Dipper, by which the Greeks sailed. The
choice was not exactly simple, of course, in an age in which the
precession of the equinoxes had not as yet fixed a Pole Star as a
recognizable center of the northern skies.
While Thales's astronomy seems to have been limited to just
such large-scale applications, the inquiries of Pythagoras
Euphorbus are obviously probing deeper, moving through appli
cations toward general laws. Not only that: they are discover
ing the grounds for the kinship among disciplines. Astronomy
and geometry emerge like twin Minervas from the designs taking
shape under Thales's staff. And along with them, by a fragmen
tary connection which will become clearer later on, there is con
cern with a peculiar ethical premise, having to do with the eating
of meat.
These are facets, I believe, of a unified archaic consciousness.
They reflect in interplay among older topics?astronomical,
meteorological, mythological topics, such as those appearing in
Hesiod's Works and Days?together with the newfound ability
to diagram these ancient stuffs along lines which defined their
intellectual significance. So we begin with the stars. We begin
with star-myths and Hesiod, and we will let the intellectual re
finements which Pythagoras introduced come out as they will in
the course of the narrative. Although it may seem prodigal to
stop to look for Pythagoras among the constellations, I think that
that's where his trail can best be picked up.
VII
Orion and his dog Sirius, Bootes and the Great Bear, the
Pleiades and Hyades, with whom Homer is well acquainted, take
on highly schematic positions in Hesiod's account of the annual
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rotation of the heavens. The astronomical knowledge of the
misplaced Boeotian farmer whose family origins lay in the East
is in no way inferior to that of the metropolitan Babylonians;
and, somewhat inexplicably, it does not differ in essentials from
a body of observations in which all western Asiatics and the
Egyptians as well seem to have shared. Perhaps the one great
difference is this, that in the fastnesses of Oriental ziggurats po
litical omens were sifted from the stars; whereas for Hesiod, in
spite of his brooding pessimism, nothing more sinister is to be
watched for in the heavens than the sunrise setting of the Ple
iades, which only meant that the season was approaching when it
would be prudent to bring the ships up from the sparkling sea,
to pull out the bilge-plugs, brace the hulls with stones, and hang
sails and rudders indoors for the winter.
Only in the Hellenistic age did astronomy become learned
enough, and ingenious enough, to perfect orthodox astrology and
Ptolemaic celestial mechanics. Only in the fourth century B.C.,
according to Otto Neugebauer, did the Zodiac, with its very an
cient constellations, reach that state of organization which it dis
plays in our morning newspapers. Pythagoras, thus, is backwards
by two good centuries from a peak of folly in astronomical think
ing, and is by the same token just so much a closer relative of
Copernicus than the run of sky-readers?Aristarchus of Samos
always excepted?during twenty intervening centuries. This is
no vain boast. Pythagoras's system in all likelihood was not
geocentric. If the earth did not move in more complicated ways,
it appears, according to the theory published by Philolaus, to have
revolved around the true center of the universe, a Central Fire
which lay always out of sight behind it, and in which the sun may
have had replenishment in its nightly journey back to the eastern
horizon.
Although cosmic questions remained unsettled, the skies them
selves had exhibited in the constellations an array of designs
which made indelible impressions on generations of wakeful hu
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PYTHAGORAS OF SAMOS
man beings. They were geometric impressions, geometric in a
special but exact sense of the word. Unfortunately for us, the
sky-charts which have been preserved are not ancient, and conse
quently they have pictured, not the old archaic images, but the
ponderous beasts and heavily attired human personages of Ren
aissance scientific art. We will do well to try to revisualize the
constellations. When we look for the Lion, the Ram, the Bull,
the Swan, or for Orion or the Virgin, what we should expect to
see are figures resembling those which in pre-Pre-Classical times
were sketched in paint on vases, engraved on seal-stones, drawn
with a minimum of strokes on a thousand different sorts of sur
faces. After all, the constellations mainly are the creatures of
Geometric art in its early Orientalizing phase. And they are,
equally, the beasts and birds and heroes of the earliest myths and
the earliest fables.
To the trained archaic eye the things looked like what they
were called. The serpent constellations, for instance, are sinu
ously extended star-meanders, of which Draco for us in the north
is a vivid example. In Scorpio we still can see the likeness of a
scorpion such as might have been scratched on an Island gem;
and in the Bird, which was later arbitrarily translated into the
Cygnus of the story of Leda and the Swan, we are reminded
of what it probably was at the start?a simple Crosshatch of the
wings and body of a large bird in flight, a crane as likely as not.
The lion which dominated the early outburst of Oriental styli
sation in Greek vase-painting is always drawn as a formidably
arch-necked beast, maned or unmaned, with compact forequarters
and a lolling tongue: what better than the tense sickle of bright
stars?the sickle is the oldest of mutilating weapons?to show
the King of Beasts in summary fashion, as it does in the constella
tion which we still call Leo?
Some of the animals, on the evidence of Aratus, seem to be
visualized in a recumbent position, with the head turned round
backwards above the body, pointing toward the hindquarters.
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The pose transfers itself into a compact composition suitable for
filling a small area, such as the shoulder of a Wild-Goat-style
vase, or the surface of a seal-stone, or a patch of black sky, or a
sand-box abacus. This is the coherence apparently of the Ram
and the Bull, possibly even of the Lion.
In contrast with the compressed menagerie, there are figures
that spread out, of which Orion is doubtless the most resplendent.
It is his belt, of course, the tightly cinched band of three stars,
which for millennia has been the unmistakable mark of the gi
gantic hunter. But a narrow belt, noticeably cinched in, has the
closest of associations with heroic naked men, warriors or wor
shippers or inscrutable adventurers, in large reliefs and small
bronze statues from Minoan times down to the end of the archaic
age. Seeing the belt, the knowing eye would supply the whole
figure.
"How many pebbles are required," asked Eurytus the Pythag
orean, "to imitate a man? How many for a horse?" What he is
apparently thinking, as Aristotle suggests, is that figures of all
sorts may be visualized as sketched out on a framework of points,
which could be indicated by pebbles arranged on a patch of hard
sand, just as are the figures of geometry; just as are, on a larger
scale, the surveyor's boundary stones on an odd-shaped farm;
and just as are the star pictures in the sky. Archaic art, in fact,
achieves what we regard as its admirable style because it is willing
to move in summary fashion from point to point. The story is
told that two sculptors, the famous Theodoras of Samos, already
alluded to, and his brother Telecles, collaborating on an archaic
wooden statue of Apollo, worked one on one half of the statue
in Samos, the other on the other half in Ephesus, and yet when
the two halves were brought together the whole had the appear
ance of being the work of one man. We may presume that they
were not bound to a rigid "canon" or pattern of art, but that, after
agreeing on a model, they could translate it into whatever number
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PYTHAGORAS OF SAMOS
of points it would take to make a layout of the figure they had in
mind, transfer the points to the rough wood, and start carving.
What I am saying is of course that the archaic image is a crea
tion of Democritus's much-disputed Convention, as also of Anax
agoras's celebrated Nous: an act of the archaic Mind supported
by the imaginative trick of being able to see that which is sug
gested, though for inexperienced eyes nothing of the sort appears
to be really there. The evasive shape of a constellation, however,
often seems to become somehow solidified by the mythology
which surrounds it. At this point symbolism, along with a sense
of the myth behind the symbol, comes to the aid of us who are
only casual astronomers. The circlet of brilliant stars which is
called Corona, for example, "is Ariadne", according to Vitru
vius: in this case only the symbol, not the woman herself, is to
be seen. But Corona, so described, brings up the whole tragic
narrative of Ariadne, the recipient of Amphitrite's crown, her
suffering at Theseus's hands, and her marriage finally to Diony
sus. If along with this one has in mind the Ionian dances that
were danced in her honor in Delos, and the festive rites in Naxos,
she becomes all that Walter Otto has claimed for her; and as
the fairest and saddest of women, she can properly disappear in
the symbol which is her crown.
One of the better-known eccentricities of Pythagoreanism is to
claim symbolic meanings for geometric figures, for numbers them
selves, and for many haphazard objects. The relish for symbols
was indulged in with increasing abandon as a cult grew up, until
in the course of the centuries the irrationality of the whole pro
cedure becomes astonishing. But there are several levels of
irrationality, some of which undoubtedly attach themselves in no
trivial way to the earliest investigations of Pythagoras, as well as
to almost all serious inquiry. The original seat of the trouble
may have lain in the stars. I want to look at two possibilities:
one, the fables associated with the polar constellations; the other,
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the r?le of Heracles in connection with the configuration which
bears his name.
The wheeling motion of the northern stars, "which never
drown in the sea", is the key to ancient speculation, be it mytho
logically high-flown or coldly scientific. One way, it ends in
geometrical projections; the other way, it produces a pursuit
fable of not too mystic a psychoanalytic impact, which Jung calls
"the negative supraordinate personality". The basic fable, which
is traced back to Hesiod, tells us that in life the Great Bear
was a young huntress named Callisto who hunted wild beasts on
the mountain in company with Artemis. One day she chanced
to arouse the desire of all-seeing Zeus, who did what Zeus does
on such occasions. Some time afterwards, Artemis, noticing the
mark of Callisto's ensuing pregnancy while she was bathing,
turned her into a bear, to be herself hunted, until Zeus out of
pity put her among the stars. But even there her suffering con
tinued: "Behind the Bear," Aratus says, "like one who drives
her, comes the Bear Warden, who is also called Bootes. . . ."?
who had been in life the child whom Callisto conceived in her
mishap with Zeus, a boy that Callisto's vengeful father had
butchered and served up to Zeus at table.
And so together they go round and round forever. The story
has the elegance, as geometers like to say, of the most rarefied
of Olympian myths. It is also properly troubling. And when
that happens, people usually look around for a substitute myth
which is more tolerable: after the Apollonian assertion comes
the Dionysiac escape; after the cosmic oracle, the homely fable.
In the case of Bootes and his mother, people early decided against
the very premise of the Great Bear; they chose to believe that
the constellation looked more like an oversized cart, a wagon or
wain of some sort. (To us, since it's changed its shape a little,
it looks like a dilapidated dipper.) In any event Bootes, in this
alternative, could be taken as the driver of the ox pulling the
Wain. Which could inspire fables of a different order:
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PYTHAGORAS OF SAMOS
An ox-driver was driving his wain along the track, Aesop
said, when he let it slip sidewise into a deep ravine. Seeing
the trouble he'd got himself into, he started praying to
Heracles at the top of his voice. Suddenly Heracles ap
peared in the track beside him. ?Get down there and put
your shoulder against a wheel and lay on with your whip,'
Heracles said. The gods will hear your prayers better
when they hear you bellowing at your ox.'
The myth of Callisto has a logical circularity, a final inde
terminacy, which is as old as anything that can be thought of; the
myth of Heracles, whose constellation dominates the summer
skies, is exactly the opposite, in that it represents not the
workings of the prehistoric mind, but rather the exploitation of
pseudo-rational possibilities which developed later on. Heracles,
though a popular figure in very ancient art, is by no means an
early comer to the heavens. For Eudoxus-Aratus, even for
Vitruvius, the man imagined to be seen in his stars was a nameless
phantom Kneeler, a care-worn, toil-worn, pain-worn shadow of
someone who could have been anyone, perhaps any of us. But
just as Heracles gradually acquired a twelve-chaptered story
relating and systematizing his labors, so the Kneeler became the
Heracles whose labors were superimposed upon the twelve signs
of the Zodiac. According to Plutarch, he became a Sun God, a
variant on the Egyptian god Set.
From this there resulted some foolishness in later antiquity
which is most pertinent to our story. Another passage in Plu
tarch, which in my opinion displays how complete was the collapse
of the Pythagorean tradition, asserts that adherents of the cult
believed this Sun God to be a demonic power; that whereas the
triangle belongs symbolically to certain deities (Hades, Dionysus,
and Ares), the quadrilateral to others (Rhea, Aphrodite, De
meter, Hestia, and Hera), the dodecagon to Zeus, the polygon
of fifty-six sides belongs to Heracles-Set, "as Eudoxus has re
corded". All of wrhich must be construed as utter confusion.
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Poets have made Heracles the butt of comedy; and sometimes
again the subject of great poetry, from Panyassis, the uncle of
Herodotus, to Yvor Winters. Nevertheless, the demonic powers
with which he was mantled, together with the loss of meaning
in the geometrical properties assigned to him as pr?sider over
the visible heavens, are evidence of the calamity which overtook
the Pythagoreans. Mystical geometry attracted them in much
the same way as did the murky ritual of the blood and the mirror
and the moon which is recounted in Suidas. We should be able
in a moment to deal constructively with the geometrical con
fusion. Meanwhile, in view of the sequence of the events we
have noticed, we must suspect that doctrinaire mysticism, such
as the Orphism sometimes associated with the earliest Pythag
oreans, is probably much more a late miscarriage of Pythagorean
philosophy than it is, as has sometimes been argued, an instrument
of its inception.
The fabric of geometry, as I think we shall see, was originally
a well-woven, very firm stuff.
VIII
Once when the philosopher Aristippus was shipwrecked, he
struggled up out of the sea onto a sandy beach with some com
panions^ and then, discovering geometrical designs drawn in the
sand, he cried out, according to Vitruvius: "We can be of good
cheer I see the traces of man "
He had every reason to feel cheerful. The story goes on to
say that the castaways and the natives of the place, Rhodes, em
braced one another, each cherishing the other because of their
mutual ability to converse in the language of geometry. Back at
home in Cyrene, Aristippus got into the habit of saying: "Young
people should be provided above all with the sort of wealth that
can swim with them, even from a sinking ship."
We can reconstruct how the initial discussions of geometry
went. Out of all of the shining indelible star-figures in the sky,
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and all of the parallel circling motions which the constellations
traced, the underlying simplicity of some aspects of astronomy
suggested a kind of thinking in which there was not so much the
wonder and sorrow of myth as a sudden, crystal-clear recogni
tion of a starkly familiar landscape, a landscape of surveying and
navigation and mechanical constructions. One constellation, the
Triangle (Deltoton for the Greeks, Triangulum for the Latins),
seems to have provoked exclusively geometrical associations;
Aratus's short sentence about it describes it as an isosceles triangle.
The inference to be drawn is that sky imagery is the key to the
archaic intuition of what a point and line, a triangle and other
several-sided figures, fundamentally are.
"A simple line," says Sextus Empiricus in a clear-cut reference
to the earliest geometers, "is conceived as drawn from a point to
a point." It is, as it were, the illusionary tie between two stars,
the "lines of light" which Aratus saw in Cassiopeia; or, in much
the same way, the fading impression in the dust made by a cord
stretched between two stakes. Similarly, as Sextus adds, lines
drawn from one point to another to a third point and back to the
first enclose a plane which is triangular in shape; and if lines
from the three points are connected with a fourth point lying
above the triangle, the result is a solid figure, a pyramid on a
triangular base. And so on for other figures, a cube, for example.
So then, if a straight line can be evoked in the mind's eye by
a cord stretched from a point to a point, a curved line can be as
easily projected by the swing of the tip of a stick at the end of
a tether fixed to a pivot or looped around several pivots. Geome
try in practice was at first an art of cord-stretching, as Democritus
himself describes it: a landscaping art which was useful to
builders and fascinating to study on an improvised abacus on a
seashore.
But while the stretched cord could be converted into the ruler
and compass and plumb-line of a Pythagoras, or a Vitruvius, the
similarity of earth-based constructions with astronomy would have
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been missed by no one, and we do know definitely that the like
ness of earth figures and sky figures had impressed another poly
math, Archytus, a contemporary of Democritus, whom Horace
celebrates in a moving ode: "Measurer of the sea and land,/And
unnumbered grains of sand. . . ."
The eye of Archytus had caught the perfectly curving orbits
which a sort of toy, a Whirler, produced when boys swung it
around at the end of a string at certain festivals, and his ear had
caught the change in pitch in the whistling sound which the toy
emitted as it traveled faster and faster. The curve of its flight,
he implies, is related to that of each of the heavenly bodies: he
had already noted the mathematicians' discernment of the speeds
of the constellations, rising and setting. The sounds which the
Whirlers made, moreover, in addition to being steadier than
ordinary sounds, resolved themselves into ratios which reflected
systematically the speeds at which the Whirlers were moving.
Here was an interplay of curved flight-lines and speeds and
sounds and forces, with a mathematics of its own, yet obviously
reflecting the new realization of the definite arithmetic ratios in
the attunement of a lyre. For Archytus, or someone a little later
than he, or a little earlier, perhaps the stars were Whirlers afar
off, sounding tones of their own, which might be called the Music
of the Spheres, with no primary aesthetic meaning intended.
In the beginning geometry went back and forth to and from
the stars. But before long, Sextus Empiricus goes on to say,
busy minds began playing with the idea that a simple line should
be more fully rationalized than these first archaic intuitions had
provided for. A line must be created, the Eleatics began to think,
by a point flowing in motion, or if not that, then by points lying
side by side, shoulder to shoulder; and a plane would be a line
flowing in crosswise motion, or a whole field of points. But what
then was a point? An imponderable abstraction, it seemed, which
could be pursued only into the absurdities of the paradoxes of
Zeno or the rigorous atomism of Democritus. Or resigned to
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the supernatural: where disembodied Forms replaced simple
stars.
But before that impasse loomed ahead, a triangle, the triangle,
was simply a Deltoton constructed out of the imaginary?the
Anaxagorean?lines that flew "straight and swift between the
stars", in the phrase of Wallace Stevens, whose point in the poem
is to praise the imaginative Anaxagorean concept. Furthermore,
it was the right triangle in a semicircle, isosceles or scalene, which
revealed itself, according to Callimachus, most delicately in the
sand under the nub of the Sage's staff. Which is to say, the tri
angle of the Great Theorem.
IX
I abstain from discussion of the Pythagorean Theorem. Its
place in history is familiar and clear. One of its beauties is that,
like the equivalence of the angles of any triangle to two right
angles, the proof is self-evident. At least, in several elementary
constructions, I think it is, and even the classic Windmill con
struction of Euclid I, 47, seems to have a transparency of its own;
or, perhaps, interest as a suspense thriller. Be that as it may,
Thomas Hobbes, having reached the age of forty with no knowl
edge of geometry, happened to notice this proposition on the page
of an open book while he was waiting in a gentleman's library.
"By God," said he, as John Aubrey tells us (adding that Hobbes
would swear now and then by way of emphasis), "this is im
possible " So he read the page again, checked back to some
earlier propositions, and ended "in love with geometry".
Like the right triangle the pentagon is a potent ancient sym
bol for PYTHAGORES OF SAMOS. Lucian's gibe to the
effect that "four is ten" evokes the wonder that can be worked
with pebbles and a staff on a patch of sand beside the sea. It
meant something that looked innocent enough when the sun
and-wind-burned philosopher put his markers down like this:
(. + .. + ... + ....) equals ten. But when he arranged the peb
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bles another way they represented a triangle which began to
hint at a mathematical chasm. Then, on top of that, came a
second design, equally powerful, equally disconcerting, which
Lucian describes in a short fantasia called "Slip of the Tongue".
The first was a triangle of indeterminable dimensions. The second
was the star pentagon:2
Of each it might be said that this is Pythagorasy in the sense in
which it was said that Corona is Ariadne; and just as the Crown
signified all womanly beauty and sadness to the knowing, so, ap
propriately enough, the star pentagon came down to the more
knowing Pythagoreans signifying manly health.
The special power of the pentagon lay in its ability to function
as one of the twelve surfaces of a regular solid called a dodecahe
dron, which acquired a dazzling reputation as the "cosmic figure"
that was thought to picture best the geometric structure of the
universe. To an eye, not the archaic eye alone, the dodecahedron
can suggest a cosmos, on the sagging facets of which the constella
tions (or galaxies) are spun precariously, as I hope my flat little
supplementary sketch will suggest.3
The twelve-sided globule, though, is not exclusively a creation
of the geometer's art. This particular solid, like the cube and
the single and double pyramids, existed as an archaeological fact,
^he pebbles forming an equilateral triangle on the left above illustrate the
tetraktys "four is ten", in which the perpendicular is the irrational square root of 3.
The pentagon within the star on the right is constructed on the irrational square root
of 5, the diagonal of two squares lying side by side.
^he dodecahedron on the left is in its normal shape and on the right in its
flattened shape when it is exploded and stretched out uniformly to give the illusion
of the array of the kosmos which covers us.
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PYTHAGORAS OF SAMOS
according to Cantor, wrell before the day of Pythagorean geome
try. And it continues to exist at the present time in the form of
decorative, star-pointed, glass-and-tin, suspended lamps, coming
apparently from Arabic sources, through Spain, to the artisans of
contemporary Mexico.
The cosmic import of the pentagon rises to its true height,
however, when it is combined with an equilateral triangle and
inscribed in a circle, yielding an equal-angled fifteen-sided figure.
And this wondrous thing, though its significance seems to have
faded early in the annals of the Pythagorean cult, is nevertheless
the mainstay in the analemmay Vitruvius's (and antiquity's) com
plex sundial, which recorded not just trivialities like the hour of
the day, but the day of the year, the number of days back to the
solstice and ahead to the equinox. The analemma diagrammed
the morning on which Sirius could be expected to make its helia
cal rising: an event of great significance in Egypt, for instance,
because of the agriculture bordering the majestically fluctuating
Nile, and in Samos somewhat similarly, because of certain ancient
vegetation festivals. It could do this, and more, because the base
where the shadow which the sun cast from the tip of the gnomon
was circumscribed in a way which corresponded in its fifteen di
visions to the tilt of the ecliptic. The angle of the ecliptic was
taken, in other words, to be one-fifteenth part of a circle, or, as
we started saying some centuries later, 24 degrees. By reading
the position of the sun according to a shadow on a scale of this
range, the observer of the analemma had a well-wrought almanac
spread out at his feet.
"With regard to the last proposition," writes Proclus at the
conclusion of Euclid Book IV, "in which he inscribes the side of
the fifteen-angled figure in a circle, for what object does anyone
assert that he propounds it except for the reference of the prob
lem to astronomy? For, when we have inscribed the fifteen
angled figure in the circle through the poles, we have the dis
tance from the poles both of the equator and the zodiac, since
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they are distant from one another by the side of the fifteen
angled figure."
Probably no one person "discovered" the angle of the ecliptic,
since it was a phenomenon which would have been observed in
tensively all over the world in connection with the study of the
solstices. But the sun's slow teetering path through the celestial
sphere, as stimulating as it was to the seasonal awareness of
people in Yucatan, at Stonehenge, on the islands of Syros and
Tenedos, in the Nile valley and the Euphrates, could not have
come in for close description, let alone a measurement of the in
clination to the celestial equator, until some way of diagramming
earth-sky relations came into being. The solution of this problem
I think can reasonably be attributed to Pythagoras himself. The
fifteen-sided figure is geometry and astronomy simultaneously:
it transposes one thing into another, triangles and pentagons into
the circle of the zodiac, in accordance with the well-known belief
of the Master in the interrelatedness of all parts of the cosmos.
In analyzing the geometry of the ecliptic angle, Pythagoras
would have had a good amount of crude data at hand. Hesiod,
for instance, who is detailed and sufficiently precise in charting
the course of the sun from solstice to solstice, introduces the
word "tropic" as the technical term for its turning-points in sum
mer and winter, with full implications as to the zones and the
curvature of the earth; while the measure of the angle is at
tributed in the A?tius summary to Pythagoras himself, though
this claim did not go unchallenged. The real difficulty, of course,
was to find a way to speak of the angle, or even to think precisely
about it. If the mere size of the sun gave so much trouble to
the pre-Socratics?"bigger than the Peloponnesus . . . ", "28
times the size of the earth . . . ", "broad like a leaf . . .", "no
larger than a man's foot . . ."?in comparison with these di
mensions, the fifteen-angled figure in a circle is a marvel of
precision.
Unfortunately it is more accurate as geometry than as as
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PYTHAGORAS OF SAMOS
tronomy, although the small error of a fraction of a degree went
undetected until the time of Eratosthenes. The fifteen-angled
grid served well enough for the analemma; and maybe that's
as much as should be required of it. It was accurate "for all
practical purposes", which is a standard hard to improve on, since
no unchanging, absolutely accurate value could ever have been
stated for it. Here again, Pythagoras's postulate that all of the
gears of the universe meshed smoothly together seemed to showr
under further testing some wheels that were seriously misshapen.
X
But before the evidence of the fallibility of the system turned
up, Pythagoras had tried to bring all facets of the archaic con
sciousness into harmony, one program with another. To be a
cosmologist, which Pythagoras eminently was, meant just that:
a kosmos being that which held all things in due order, mind and
matter. And so, to the drawings on the paths of the sanctuary at
Didyma there is to be added an ethical structure of which Callim
achus also is mindful.
The connection of the stars with human conduct is ancient, and
not necessarily so frivolous as astrology would like to have us
believe. The author of the Titanomachia made the centaur
Chiron, in his r?le as teacher of mankind, bring to the human race
a knowledge of "oaths, holy sacrifices and the patterns of Olym
pus". These most important "schematics of Olympos" are the
constellations, "the identification and mythology of which," says
G. L. Huxley, "formed a substantial part of early Greek hexa
metric poetry." Substantially the same threads of ethics and
astronomy are interwoven in Hesiod's Works and Days.
In the sum and substance of his teaching, Pythagoras, like
Hesiod advising his brother Perses, censured the use of violence.
For Hesiod the doctrine of moderation springs from a haunting
recollection of the "ages" and "races" of men: in a good age, a
golden age, men did not act toward one another like wild beasts
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and birds of prey, not like the hawk toward the nightingale in
the fable. Men lived happily together on the grain-giving earth
until the earth covered them and they were succeeded by another
race. A virgin daughter of Zeus, Justice, moved among them.
The story of the successive ages of men is retold as a constellation
myth in the Eudoxus-Aratus shorter variant of the Hesiodic
poem, where the application has become clearly Pythagorean:
as in the Metamorphoses y Ovid's sacrificial ox with gilded horns
eloquently protests.
The maiden Justice in this version is the constellation Virgo.
She is "set among the stars not far from far-seen Bootes", says
Aratus, because when the "race of bronze" came along in its un
happy time and gave swords to highwaymen and began devouring
its ploughing oxen, she could no longer abide mankind. She fled
to the starry heavens, where, embodying dike, she represents
cosmic balance, or, in ethical terms, disciplined self-restraint and
peaceableness.
Thinking of this kind is transparently the basis for Pythagoras's
injunction against eating meat. As an article in the poetic archaic
code, the prohibition is a figurative way of condemning disorder
and of dramatizing cruel and reckless conduct by making the act
of a man butchering his ploughing ox a symbol of self
destruction. It bears no resemblance to a taboo. There are archaic
fantasies and digressions and folk platitudes in Hesiodic poetry, to
be sure; but no stress on ritual as such.
Our problem hardly consists in trying to evaluate the abstract
virtue of eating or not eating meat. All that is bad about killing
amiable beasts is abstractly as self-evident to any sensitive person
as the angle of the semicircle; our problem is to inquire into the
extent to which the prohibition was literal or symbolic. For
Ovid, Pythagoras and this counsel supply the substance of the
greatest poetry in a great poem. The Pythagorean ethic in effect
motivates a backwards gentle glance over intense ages and intense
lives lived briefly and then metamorphosed. This is the impor
3
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PYTHAGORAS OF SAMOS
tant matter. On the whole I think it is irrelevant to speculate
seriously on Ovid's, or Pythagoras's, personal dietary habits.
But I defend the symbolism in its entirety.
The rule holds good?things are one; living things are one.
We do not eat ourselves. (Consequently it could follow that
beans, because they resemble testicles, wrere habitually pronounced
unacceptable as diet; and wool, as a product of life, unsuitable
for shrouds.) Under the rule of oneness, we undergo only a
transmigration from ourselves upon our deaths. Nothing is cre
ated or destroyed. This root principle, often reiterated among
the archaic philosophers, states as much as needs to be stated about
the doctrine of the transmigration of souls. The problem again
is the degree to which it is symbolic. Certainly, I venture to say,
it is not to be taken literally, though modern scholars from Zeller
to Guthrie have tended to take it so. As a doctrine of Pythagoras,
it is voiced first in a satiric context by a great Ionian, Xenophanes:
"When that puppy cries when somebody beats him, I hear the
voice of my dear friend." How better to gibe at one who believes
explicitly, as Pythagoras obviously did, in the oneness of life
But gibing is a sport which is pleasant enough in Xenophanes,
and in Lucian, and in Ben Jonson. Metempsychosis, somewhat
similarly, offers the poet an aesthetic device, as in Callimachus?
or exaggeratedly in Empedocles; or in Shakespeare when he
wants a character to brood on Shylock's apparently wolfish appe
tites; or in Joyce in the act of creating an Irish Ulysses. Metem
psychosis besides seems to have been the dull-witted teacher's
rhetorical substitute for the true concept. In any event, one of
the best of the Renaissance neo-Platonists, John Reuchlin, in his
study of Pythagoras, rejected literal transmigration, as do most
close readers of the ancients-?Albin Lesky, for instance. Specialist
scholars have a bent for delving so deeply into a question of this
kind that they find it difficult to straighten up and look around.
Because of this seemingly austere and impersonal ethic, it has
been supposed that the Pythagorean community, when it comes
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dimly into view in Italy after Pythagoras's migration, must natur
ally have been a fraternity of Spartans. If being Spartan means
being hardy and disciplined, the citizens of Crot?n, Pythagoras's
adopted city, appear to have qualified for the honor, which never
theless remains dubious. When they managed to destroy the
Sybarites, those special fondlings of luxury, they were led against
them by Milon, the famous wrestler, reputedly a follower of
Pythagoras. Now this Milon, whether or not because of the
training his master had given him, was six times a victor in the
Olympic games, six in the Pythian, ten in the Isthmian, nine in
the Nemean, when previously the Crotonites had become inured
to winning none at all. He is moreover the most renowned glut
ton in history. He ate twenty pounds of meat, twenty of bread,
and drank eight and one-half quarts of wine a day; he carried a
sacrificial ox the length of the Olympic stadium, slaughtered it,
roasted it, and devoured it ail by himself in one afternoon. His
ethic cannot be described as austere or impersonal; the ways of
gladiators seldom are, whether they are Crotonites or New York
Jets. It is ironical, too, that Milon's triumphs, in the earnest
judgment of Vitruvius, were worthless in comparison with the
humane achievements of Pythagoras and the philosophers.
And as it happens Milon was not the only Crotonite champion
who appeared at this time. Since on one occasion some six or
eight teammates of his won first places at Olympia, something
more than an ethic must have been at work among the young
men of the city. A science of physical conditioning had quite
certainly been built up among the Crotonite physicians, among
whom was the much-sought-after Democedes, who later migrated
to Samos. According to Athenaeus, athletes were taught to eat
with more than normal heartiness while undergoing intensive
gymnastic exercises. The result speaks for itself. In Pythag
oras's time the development of pragmatic sciences in civic life
was a lot more impressive, I'd say, than the practice of asceticism.
Nor is austerity apparent in the Pythagorean tradition. Ionian
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enjoyments, Ionian excitements, Ionian intellectual poise, con
tinued evidently to govern the lives of the successors of the trans
planted Samian. Eudoxus of Cnidus and Archytus of Tarentum
were worldly men, polymaths, and ruling powers in their cities.
Eudoxus, for whatever it is worth, is reported by Aristotle to have
been a hedonist; and indeed the seat of hedonism, the Cyrene of
Aristippus, produced more than its share of the later Alexandrian
masters of the old Ionian arts. But if the pleasure principle was
adhered to, it was adhered to (theoretically, anyhow) with re
serve, with common sense, with a sort of gallantry; because, after
all, the real heirs of Pythagoras?ignoring most of the chattering
cult?were Democritus, Epicurus, Lucretius, and a multitude of
gifted, peaceable men in later times, including Gassendi and
Thomas Hobbes.
But Pythagoras undoubtedly did found a school in Crot?n in
which membership entailed closer adherence to a code than is
expected of an audience attending lectures. The evidence for a
Brotherhood is as overwhelming in its gross weight as it is a
hodgepodge of hearsay. We may suppose, as T. J. Dunbabin
did, that the Samian exerted a personal magnetism which drew
a tight band of followers around him. Such a group would not
be likely to be either democratic or aristocratic, since there was
not a popular tyrant at work in Crot?n, nor an ambitious landed
gentry. It could have been a more or less exclusive club which
engaged, in the manner of the age, in philosophic inquiry, sports,
and broad political action. Since we assume that Pythagoras
was uniquely responsible for it, it follows that he imported the
seeds for founding a society of this sort from Samos; and in that
event we can hardly suppose that the habit of pursuing free in
quiry which he had formed in Ionia would suddenly give place
in Italy to the cultivation of mystic or fraternalistic rituals. There
must be a middle ground which is still to be explained.
Up to this point we have been saying of the archaic cosmolo
gist: How grand the aspiration to combine all of the arts and
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sciences?arithmetic, astronomy, music, geometry, physiology
and how sad to discover that they don't always combine smoothly.
In this predicament the cosmologist may suspect that in the end
they won't combine in any ordinary way at all. He will tell him
self at first that this is the fault of his pebbles?they are too
coarse; his compass-dividers are not sensitive enough to make
fine discriminations. But at some point he will begin to realize
that the grand scheme he is in search of probably cannot be laid
out on a beach, that it can only be defined, through a laborious
personal effort, within the mind itself. "Every art is a system of
apprehensions," says Sextus about Pythagorean thinking. This
conviction is what the later Ionian, Anaxagoras of Clazomenae,
pushed through to one logical conclusion. From such a principle
it follows that for one to communicate a carefully ordered system
to another person, that other person must submit to its slow un
folding within his own intelligence. The seven canonic branches of
knowledge are not meaningful as external objects, but they be
come meaningful in the acts of patient explication and patient
reconstruction within the recipient's mind. Hence, I believe, the
Pythagorean motto, Silence, and the quasi-religious temper of the
Brotherhood. A doctrine of the memory of Forms (which Lucian
played with) is far beside the point, in my opinion, as is the ex
treme abstractionism of Euclidean mathematics. But it does
seem, to add up to this: that the more nearly coherent the system
envisioned, the more evasive is its final description, the more
difficult the act of communication, and the greater the need for
the concentration of the faculties, as it occurred within a Pythag
orean society. Or, for that matter, within a cloister; or, for the
matter of all that, within the tower of the Ch?teau de Montaigne,
where the books spoke and the mind worked.
For Pythagoras there came at some now-forgotten moment
the public exhibition of the inner mechanism of his system, along
with its troubles. An early follower named Hippasus is famous
for having disclosed the secret of the dodecahedron, or, if not
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PYTHAGORAS OF SAMOS
that, for having revealed the discovery of irrationals. Which
ever it was makes but little difference. Pythagoras, according to
one good reading of the Proclus "Summary", had discovered both
already, and either disclosure has the reversion to Hesiodic chaos
implicit in it. Since the dodecahedron is built of pentagons and
pentagons of irrational numbers, the same mathematical evils
came flying out no matter which of Pandora's boxes Hippasus
chanced to open.
The axiom that Pythagoras had lived by was that differentia
tion within the cosmic unity could be expressed in intimately re
lated number patterns. In saying this, I do not mean to repeat
the perverse Aristotelian formula "Things are number"; nor
even the alternative, "Things imitate number"; but to go back
to the verse phrase preserved in Sextus Empiricus, "Things re
semble number"?aArithmo de te fant* epeoiken"?-or, in defer
ence to the antiquity of the language: "Within arithmetic all
things find fitting place. . . ." There is no mystery about what
Pythagoras had in mind. His crowning theorem, in one form at
least, could be converted easily into the numbers 3:4:5 for the
sides of the Pythagorean triangle; music into the ratios 4:3; 3:2;
2:1 for the fourth, fifth, and octave; the circle of the celestial
poles into the fifteen-angled figure; the excess of darkness over
daylight always equalizing eventually with the excess of daylight
over darkness; the justice of the Virgin and her Balances ruling
the creation, pound for pound, ounce for ounce. . . . How far
could these number systems be extended? Why not throughout
the universe?
The answer turned out to be: They could not be extended,
they would not fit together even within their own immediate
provinces. The secret of the collapse of the Pythagorean con
cept?Hippasus's infamous revelation?lies in the indeterminable
nature, the "irrationality", of the diagonals of the three simplest
geometric figures, which corresponds with a menacing consistency
to the square roots of the first primary numbers. It began with
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the square root of 2, the diagonal of the square of unit value; it
continued with the square root of 3, the perpendicular of the
equilatera